Teaching presentation

Preamble

Statistics - Freedman, Pisani and Purves

Chapter 1 Controlled experiments
Chapter 2 Observational studies
Chapter 3 The histogram
Chapter 4 The average and the standard deviation
Chapter 5 The normal approximation for data
Chapter 6 Measurement error
Chapter 7 Plotting points and lines
Chapter 8 Correlation
1. The scatter diagram
2. The correlation coefficient
3. The SD line
Chapter 9 More about correlation

Correlation

The scatter plot

Review

Frequency tables
Histograms & barplots
Summary measures

What if we have two variables?

How do X and Y relate to each other?

What if we have two variables?

Quantitative vs Quantitative

\[\begin{array}{c|cc} \hline i & X_i & Y_i \\ \hline 1 & 9.4 & 11.2 \\ 2 & 9.8 & 10.4 \\ 3 & 11.6 & 10.4 \\ 4 & 10.1 & 10.1 \\ 5 & 10.1 & 9.4 \\ 6 & 11.7 & 11.8 \\ 7 & 10.5 & 10.5 \\ 8 & 8.7 & 8.0 \\ 9 & 9.3 & 10.7 \\ 10 & 9.6 & 9.5 \\ \hline \end{array} \]

Height and weight for individuals.
Testosterone levels and race times for athletes.
Sun exposure and number of branches for plants.

What if we have two variables?

Qualitative vs Quantitative

\[\begin{array}{c|cc} \hline i & X_i & Y_i \\ \hline 1 & A & 11.7 \\ 2 & B & 10.5 \\ 3 & A & 8.7 \\ 4 & B & 9.3 \\ 5 & B & 9.6 \\ 6 & A & 11.2 \\ 7 & B & 10.4 \\ 8 & B & 10.4 \\ 9 & B & 10.1 \\ 10 & A & 9.4 \\ \hline \end{array} \]

Eye color and vision scores for individuals.
Industry and share price volatility for businesses.
State and student ATAR scores for universities.

What if we have two variables?

Qualitative vs Qualitative

\[\begin{array}{c|cc} \hline i & X_i & Y_i \\ \hline 1 & A & Z \\ 2 & B & Y \\ 3 & A & Z \\ 4 & B & Y \\ 5 & B & X \\ 6 & A & Z \\ 7 & B & X \\ 8 & B & X \\ 9 & B & X \\ 10 & A & Z \\ \hline \end{array} \]

Political preference and suburb for voters.
Favourite music genre and shirt color for music fan.
Car brand and shampoo choice for customer.

How do X and Y relate to either?

Quantitative vs Quantitative

Data example

Drawing

How can we find out if our cereal is "good" to eat?

Australian food nutrient database
http://www.foodstandards.gov.au
5740 foods
54 nutrients
117 are breakfast cereals

Scatter plot

What is the relationship between Energy (Kilojoules) and the amount of added sugar?

Scatter plot

Differences in association

Prediction

Exploring more variables

Summary

We can use scatter plots for visualation of two variables

We can use our eyes…

1. to test a hypothesis.
2. to make a prediction.
3. to explore a set of data.

Caveats

1. We often see what we want to see.
2. A plot does not quantify a relationship.
3. We can only look at so many plots.

Epilogue

Presentation generated with ioslides in RStudio.
Fully reproducable.
Available on github:
https://github.com/ellispatrick/Presentations/Teaching

R version

sessionInfo()

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